A consol, issued by the British government to finance the Napoleonic Wars is an example of:
A an ordinary annuity.
B perpetuity.
C growing annuity.
D annuity due.
The correct answer and explanation is:
The correct answer is B. perpetuity.
A consol is a type of bond issued by the British government, especially during the Napoleonic Wars, that pays a fixed interest forever. The defining characteristic of a perpetuity is that it provides regular payments without an end date. In the case of the British consol, the bond promised to pay interest to the holder for as long as the government existed, with no set maturity date.
A perpetuity has a constant, indefinite cash flow, making it different from other types of annuities, such as ordinary annuities, which make payments over a fixed period, or a growing annuity, where the payment amounts increase over time. The key feature that distinguishes a perpetuity is the unlimited duration of the payments. In the case of the British consol, the bond offered annual payments (interest) that continued indefinitely, making it an example of a perpetuity.
A perpetuity is calculated using the formula: Present Value of Perpetuity=Cr\text{Present Value of Perpetuity} = \frac{C}{r}
Where:
- C is the annual payment (interest)
- r is the discount rate or the required rate of return.
Unlike an ordinary annuity or annuity due, where payments end after a certain number of periods, the perpetuity assumes payments continue forever, hence the British government’s issuance of consols as a way to raise money without having to repay the principal.
Therefore, the consol is a classic example of a perpetuity rather than any form of finite annuity.